Parallel shear flows are susceptible to Kelvin-Helmholtz instability (KHI). In classical KHI, the shear layer forms vortices about an inflection point entraining fluid from the free-stream. Compressibility effects are known to stabilize KHI due to the pressure oscillation, which rolls and unrolls Kelvin-Helmholtz billows \cite{karimi}. In the present work, we look at the effect of rarefaction and compressibility on the development of KHI. Two-dimensional mixing layers are perturbed using a solenoidal perturbation for different Mach numbers and Knudsen numbers and simulated using a Boltzmann transport equation-based solver. Figure 1 shows the contours of the streamwise averaged perturbation kinetic energy (PKE) at Reynolds number, $Re=\Delta u \delta /2\nu_\infty = 200$ (where $\Delta u$ is the difference in free-stream velocity, $\delta$ is vorticity thickness and $\nu_\infty$ is the kinematic viscosity at the free-stream) and Mach number, $M_c = \Delta u/2c_\infty=0.2,0.8$ and $1.2$ (where $c_\infty$ is the free-stream speed of sound) as a function of spanwise distance, $y/\delta$, and time, $\Delta u t/\delta$. In the incompressible regime, the PKE is localized to the mixing layer centreline, whereas, in the compressible regime, perturbations radiate away from the centreline with faster rates of propagation seen for higher $M_c$. The present work will discuss the effect of compressibility and rarefaction on the spatio-temporal variation of PKE in KHI. REFERENCES [1] Mona Karimi and S. S. Girimaji, Suppression mechanism of Kelvin-Helmholtz instability in compressible fluid flows. Physical Review E, 93, 041102(R), 2016.